The NLO JIMWLK Hamiltonian with massless quarks [1]}, [2]}:
\(&&H_{J I M W L K}^{N L O}=\int _{\mathbf {x}, \mathbf {y}, \mathbf {z}} K_{J S J}(\mathbf {x}, \mathbf {y}, \mathbf {z})\left[J_{L}^{a}(\mathbf {x}) J_{L}^{a}(\mathbf {y})+J_{R}^{a}(\mathbf {x}) J_{R}^{a}(\mathbf {y})-2 J_{L}^{a}(\mathbf {x}) S_{A}^{a b}(\mathbf {z}) J_{R}^{b}(\mathbf {y})\right] \nonumber \\&&+\int _{\mathbf {x}, \mathbf {y}, \mathbf {z}, \mathbf {z}^{\prime }} K_{J S S J}\left(\mathbf {x}, \mathbf {y}, \mathbf {z}, \mathbf {z}^{\prime }\right)\left[f^{a b c} f^{d e f} J_{L}^{a}(\mathbf {x}) S_{A}^{b e}(\mathbf {z}) S_{A}^{c f}\left(\mathbf {z}^{\prime }\right) J_{R}^{d}(\mathbf {y})-N_{c} J_{L}^{a}(\mathbf {x}) S_{A}^{a b}(\mathbf {z}) J_{R}^{b}(\mathbf {y})\right] \nonumber \\&&+\int _{\mathbf {x}, \mathbf {y}, \mathbf {z}, \mathbf {z}^{\prime }} K_{q \bar{q}}\left(\mathbf {x}, \mathbf {y}, \mathbf {z}, \mathbf {z}^{\prime }\right)\left[2 J_{L}^{a}(\mathbf {x}) \operatorname{tr}\left[S^{\dagger }(\mathbf {z}) t^{a} S\left(\mathbf {z}^{\prime }\right) t^{b}\right] J_{R}^{b}(\mathbf {y})-J_{L}^{a}(\mathbf {x}) S_{A}^{a b}(\mathbf {z}) J_{R}^{b}(\mathbf {y})\right] \nonumber \\&&+\int _{\mathbf {w}, \mathbf {x}, \mathbf {y}, \mathbf {z}, \mathbf {z}^{\prime }} K_{J J S S J}\left(\mathbf {w}, \mathbf {x}, \mathbf {y}, \mathbf {z}, \mathbf {z}^{\prime }\right) f^{a c b}\left[J_{L}^{d}(\mathbf {x}) J_{L}^{e}(\mathbf {y}) S_{A}^{d c}(\mathbf {z}) S_{A}^{e b}\left(\mathbf {z}^{\prime }\right) J_{R}^{a}(\mathbf {w})\right. \nonumber \\&&\left.-J_{L}^{a}(\mathbf {w}) S_{A}^{c d}(\mathbf {z}) S_{A}^{b e}\left(\mathbf {z}^{\prime }\right) J_{R}^{d}(\mathbf {x}) J_{R}^{e}(\mathbf {y})+\frac{1}{3}\left(J_{L}^{c}(\mathbf {x}) J_{L}^{b}(\mathbf {y}) J_{L}^{a}(\mathbf {w})-J_{R}^{c}(\mathbf {x}) J_{R}^{b}(\mathbf {y}) J_{R}^{a}(\mathbf {w})\right)\right] \nonumber \\&&+\int _{\mathbf {w}, \mathbf {x}, \mathbf {y}, \mathbf {z}} K_{J J S J}(\mathbf {w}, \mathbf {x}, \mathbf {y}, \mathbf {z}) f^{b d e}\left[J_{L}^{d}(\mathbf {x}) J_{L}^{e}(\mathbf {y}) S_{A}^{b a}(\mathbf {z}) J_{R}^{a}(\mathbf {w})\right. \nonumber \\&&\left.-J_{L}^{a}(\mathbf {w}) S_{A}^{a b}(\mathbf {z}) J_{R}^{d}(\mathbf {x}) J_{R}^{e}(\mathbf {y})+\frac{1}{3}\left(J_{L}^{d}(\mathbf {x}) J_{L}^{e}(\mathbf {y}) J_{L}^{b}(\mathbf {w})-J_{R}^{d}(\mathbf {x}) J_{R}^{e}(\mathbf {y}) J_{R}^{b}(\mathbf {w})\right)\right]\) 
